Using Coordinates to Prove Geometric Theorems: Mastery Test

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is /10 units. The coordinates of point C are _______. The slope of CD is ________. The possible coordinates of point D are ______ and ______.

(5,2) 5 (6,5) (4,-1)

The coordinates of the endpoints of AB and CD are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which condition proves AB//CD that ?

(y4-y3/x4-x3 = y2-y1/x2-x1)

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if parallelogram ABCD is proven to be a rectangle?

(y4-y3/x4-x3 = y3-y1/x3-x1) and (y4-y3/x4-x3 X y2-y1/x2-x1) =-1

∆ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices. The measure of the longest side of ∆ABC is ___________ units. ∆ABC is _________ triangle.If ∆ABD is formed with the point D(1, 2) as its third vertex, then ∆ABD is ____________ triangle. The length of side AD is __________ units.

6 an isosceles a right scalene triangle 5

a rhombus with non perpendicular adjacent sides

A(2, -2), B(3, 0), C(4, -2), D(3, -4)

a parallelogram with non perpendicular adjacent sides

A(2, 0), B(3, 2), C(6, 3), D(5, 1)

a square

A(3, 3), B(2, 5), C(4, 6), D(5, 4)

a rectangle with non congruent adjacent sides

A(3, 3), B(3, 6), C(7, 6), D(7, 3)

A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?

A. ABCD is a parallelogram with non-perpendicular adjacent sides.

Which point lies on a circle with a radius of 5 units and center at P(6, 1)?

B. R(2, 4)

If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?

D. (4, 3)